Basic properties
Modulus: | \(6001\) | |
Conductor: | \(6001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(88\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6001.cu
\(\chi_{6001}(81,\cdot)\) \(\chi_{6001}(225,\cdot)\) \(\chi_{6001}(242,\cdot)\) \(\chi_{6001}(336,\cdot)\) \(\chi_{6001}(361,\cdot)\) \(\chi_{6001}(370,\cdot)\) \(\chi_{6001}(625,\cdot)\) \(\chi_{6001}(727,\cdot)\) \(\chi_{6001}(735,\cdot)\) \(\chi_{6001}(1143,\cdot)\) \(\chi_{6001}(1339,\cdot)\) \(\chi_{6001}(1704,\cdot)\) \(\chi_{6001}(1942,\cdot)\) \(\chi_{6001}(2129,\cdot)\) \(\chi_{6001}(2427,\cdot)\) \(\chi_{6001}(2554,\cdot)\) \(\chi_{6001}(2580,\cdot)\) \(\chi_{6001}(2665,\cdot)\) \(\chi_{6001}(2733,\cdot)\) \(\chi_{6001}(2741,\cdot)\) \(\chi_{6001}(3166,\cdot)\) \(\chi_{6001}(3175,\cdot)\) \(\chi_{6001}(3209,\cdot)\) \(\chi_{6001}(3353,\cdot)\) \(\chi_{6001}(3498,\cdot)\) \(\chi_{6001}(3532,\cdot)\) \(\chi_{6001}(3591,\cdot)\) \(\chi_{6001}(3974,\cdot)\) \(\chi_{6001}(4042,\cdot)\) \(\chi_{6001}(4127,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{88})$ |
Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((2825,3180)\) → \((i,e\left(\frac{57}{88}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6001 }(370, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{79}{88}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{35}{88}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{27}{44}\right)\) |